If f^-1 (y) is the inverse of f (x) which statements must be true?

A) F (F^-1 (x)) = x

B) F^-1 (F (x)) = x

C) The range of f^-1 (y) is the range of f (x)

D) The range of F^-1 (y) is the domain of F (x)

E) The domain of F^-1 (y) is the range of F (x)

F) The domain of F^-1 (y) is the domain of F (x)

Let us assume f (x) = 2x - 5

f⁻¹ (x) = (x + 5) / 2

f (f⁻¹ (x)) = 2 ((x + 5) / 2) - 5 = x

f⁻¹ (f (x)) = (2x - 5 + 5) / 2 = x

The domain of a function is the range of its inverse and vice versa

The range of a function is the domain of its inverse and vice versa

Therefore, statements A, B, D and E are true